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Nonlinear optics from hybrid dispersive orbits

Here in this paper we expand the technique of characterizing nonlinear optics from off-energy closed orbits (NOECO) to cover harmonic sextupoles in storage rings. The existing NOECO technique has been successfully used to correct the chromatic sextupole errors on the MAX-IV machine (Olsson et al., 2020), however, it does not account for harmonic sextupoles, which are still widely used on many other machines. By generating vertical dispersion with chromatic skew quadrupoles, a measurable chromatic function dependence on harmonic sextupoles can be observed on hybrid dispersive orbits. Proof of concept of this technique was accomplished by simulations and beam measurements on the National Synchrotron Light Source II (NSLS-II) storage ring.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Nonlinear optics from hybrid dispersive orbits

In this paper we expand the technique of characterizing nonlinear optics from off-energy closed orbits (NOECO) to cover harmonic sextupoles in storage rings. The existing NOECO technique has been successfully used to correct the chromatic sextupole errors on the MAX-IV machine [Olsson et al., Phys. Rev. Accel. Beams 23, 102803], however, it does not account for harmonic sextupoles, which are still widely used on many other machines. By generating vertical dispersion with chromatic skew quadrupoles, a measurable chromatic function dependence on harmonic sextupoles can be observed on hybrid dispersive orbits. Proof of concept of this technique was accomplished by simulations and beam measurements on the National Synchrotron Light Source II (NSLS-II) storage ring.

43 PARTICLE ACCELERATORS↗

Accelerator Physics at NSLS-II: Research Accomplishments in 2023

NSLS-II accelerator physicists provided operation support for user operations and machine start-ups, carried out routine lattice characterization, and produced regular reports on beam dynamics. The commissioning of a superconducting wiggler for the HEX beamline is complete, and the wiggler effects on beam dynamics have been studied. A Facility Improvement Project for absolute lattice characterization has been approved and funded. We implemented and tested a new orbit-based technique of lattice characterization and correction. We developed a theory to calculate the beam-induced power in ceramic vacuum chambers and a new convergence map technique for nonlinear lattice characterization. We continued working on the NSLS-II upgrade including lattice development, commissioning a low-energy complex bend prototype, analyzing beam sensitivity to various errors, implementing higher-harmonic RF cavities, studying collective effects, and assessing FEL options. We also supported lattice optimization and beam diagnostics development for the EIC project. Main research accomplishments achieved in 2023, are summarized in this report.

43 PARTICLE ACCELERATORS↗

Wavefront distortion correction in scanning tunneling microscope image

Here, we report an algorithm to identify and correct distorted wavefronts in atomic resolution scanning tunneling microscope images. This algorithm can be used to correct nonlinear in-plane distortions without prior knowledge of the physical scanning parameters, the characteristics of the piezoelectric actuator, or individual atom positions. The 2D image is first defined as a sum of sinusoidal plane waves, where a nonlinear distortion renders a curve for an otherwise ideal linear wavefront. Using the Fourier transforms of local areas of the image, the algorithm generates a wavefront vector field. The identified wavefronts are subsequently linearized for each plane wave without changing lattice orders, giving rise to distortion corrections. Our algorithm is complementary to conventional post-processing algorithms that require prior detection of real space features, which can also be used to correct nonlinear distortions in 2D images acquired by other microscopy techniques.

47 OTHER INSTRUMENTATION↗

Experimental measurements for extracting nonlinear invariants

Nonlinear integrable optics are a promising alternative approach to lattice design. The integrable optics test accelerator (IOTA) at Fermilab has been constructed for dedicated studies of magnetostatic elliptical elements as described by Danilov and Nagaitsev. The most compelling verification of correct implementation of the NIO lattice is direct observation of the analytically expected invariants. This report outlines the experimental and analytical methods for extracting the nonlinear invariants of motion from data gathered in the last IOTA run.

43 PARTICLE ACCELERATORS↗

Renormalized classical theory of quantum magnets

Here, we derive a renormalized classical spin (RCS) theory for 𝑆 >1/2 quantum magnets by constraining a generalized classical theory that includes all multipolar fluctuations to a reduced CP 1 phase space of dipolar SU(2) coherent states. When the spin Hamiltonian $\hat{ℋ}$(𝑆) is linear in the spin operators $\hat{𝑺}$ 𝑗 for each lattice site 𝑗, the RCS Hamiltonian $\tilde{ℋ}$ cl coincides with the usual classical model ℋ cl = lim 𝑆→∞⁡ $\hat{ℋ}$(𝑆). In the presence of nonlinear terms, however, the RCS theory is more accurate than ℋ cl . For the many materials modeled by spin Hamiltonians with (nonlinear) single-ion anisotropy terms, the use of the RCS theory is essential to accurately model phase diagrams and to extract the correct Hamiltonian parameters from neutron-scattering data.

magnetic anisotropy↗

Understanding sextupole

In this study, we reassess the dynamics within a simple accelerator lattice featuring a single degree of freedom and incorporating a sextupole magnet. In the initial segment, we revisit the H\'enon quadratic map, a representation of a general transformation with quadratic nonlinearity. In the subsequent section, we unveil that a conventional sextupole is essentially a composite structure, comprising an integrable McMillan sextupole and octupole, along with non-integrable corrections of higher orders. This fresh perspective sheds light on the fundamental nature of the sextupole magnet, providing a more nuanced understanding of its far-from-trivial chaotic dynamics. Importantly, it enables the description of driving terms of the second and third orders and introduces associated nonlinear Courant-Snyder invariant.

43 PARTICLE ACCELERATORS↗

Understanding Sextupole

In this study, we reassess the dynamics within a simple accelerator lattice featuring a single degree of freedom and incorporating a sextupole magnet. In the initial segment, we revisit the H\'enon quadratic map, a representation of a general transformation with quadratic nonlinearity. In the subsequent section, we unveil that a conventional sextupole is essentially a composite structure, comprising an integrable McMillan sextupole and octupole, along with non-integrable corrections of higher orders. This fresh perspective sheds light on the fundamental nature of the sextupole magnet, providing a more nuanced understanding of its far-from-trivial chaotic dynamics. Importantly, it enables the description of driving terms of the second and third orders and introduces associated nonlinear Courant-Snyder invariant.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Local chromatic correction optics for Future Circular Collider e + e −

Local chromatic correction optics are proposed for the Future Circular e + − e − Collider. These new optics assume an identical layout of the magnets at all operation energies and include a new design for the arcs, for the straight sections, and for the final focus. The arcs design is a step forward from the classic FODO lattice that achieves near cancellation up to the fourth order of chromatic and geometric aberrations. Straight sections and the final focus benefit from the application of transparency conditions and are thus minimally impacting the global beam dynamics. The final focus design includes both vertical and horizontal chromaticity correction sections, crab sextupoles, and additional specific sextupoles and decapoles for the optimization of the dynamics off-energy. Decapoles are very effective in mitigating the reduction of dynamic aperture due to synchrotron radiation. Nonlinear magnet settings are further optimized with multiobjective algorithms. The overall properties of the new optics proposed are analyzed in the presence of errors and compared to other optics designs.

43 PARTICLE ACCELERATORS↗

Terahertz electric-field-driven dynamical multiferroicity in SrTiO 3

The emergence of collective order in matter is among the most fundamental and intriguing phenomena in physics. In recent years, the dynamical control and creation of novel ordered states of matter not accessible in thermodynamic equilibrium is receiving much attention. The theoretical concept of dynamical multiferroicity has been introduced to describe the emergence of magnetization due to time-dependent electric polarization in non-ferromagnetic materials. In simple terms, the coherent rotating motion of the ions in a crystal induces a magnetic moment along the axis of rotation. Here we provide experimental evidence of room-temperature magnetization in the archetypal paraelectric perovskite SrTiO 3 due to this mechanism. We resonantly drive the infrared-active soft phonon mode with an intense circularly polarized terahertz electric field and detect the time-resolved magneto-optical Kerr effect. A simple model, which includes two coupled nonlinear oscillators whose forces and couplings are derived with ab initio calculations using self-consistent phonon theory at a finite temperature, reproduces qualitatively our experimental observations. A quantitatively correct magnitude was obtained for the effect by also considering the phonon analogue of the reciprocal of the Einstein–de Haas effect, which is also called the Barnett effect, in which the total angular momentum from the phonon order is transferred to the electronic one. Our findings show a new path for the control of magnetism, for example, for ultrafast magnetic switches, by coherently controlling the lattice vibrations with light.

36 MATERIALS SCIENCE↗

Implementing nonlinear optics from Off-Energy closed orbit at NSLS-II

To characterize the second-order (chromatic sextupole) magnet lattice with high precision, we implemented nonlinear optics from off-energy closed orbit (NOECO) tool based on the linear optics from closed orbit modulation (LOCOM) method, named LOCOM-NOECO. The preliminary numerical study indicates that 1–2% precision can be achieved for the calibration of chromatic sextupoles. Further, this accuracy could potentially help in resolving some long-standing challenges of NSLS-II (e.g., the discrepancy between the designed and measured dynamic apertures) if such high precision can be fulfilled. As an independent crosscheck, we also implemented NOECO based on the independent component analysis (ICA) method using turn-by-turn (TBT) BPM data, named ICA-NOECO. Both ICA-NOECO and LOCOM-NOECO have been successfully applied to identify the pre-dialed random errors of a chromatic sextupole family including five power supplies, and achieved the root mean square (RMS) residual error of 1% and peak error less than 2%. Moreover, to mitigate the chromatic sextupole error effect, we applied the correction and achieved significant improvements in the injection efficiency as well as the dynamic apertures.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Polarization transmission in the Hadron Storage Ring of the Electron-Ion Collider

The successful operation of the future Electron-Ion Collider is contingent on maintaining high hadron beam polarization up to 275 GeV. The Hadron Storage Ring lattice, however, features a symmetry-breaking interaction region that excites strong, nonsystematic spin resonances, posing a significant threat to polarization preservation. This paper systematically investigates two complementary strategies to ensure high polarization transmission. The first method involves optimizing the vertical betatron phase advance between Siberian snakes to orchestrate a cancellation of depolarizing kicks across the ring. We demonstrate through simulations that both dynamic and fixed-optics solutions based on this principle can successfully preserve polarization through the strongest resonances. The second, more powerful approach involves optimizing the snake rotation axes to suppress resonance driving terms at their source. We revisit established symmetric configurations, such as the Lee-Courant schemes, and introduce a novel, highly symmetric “Doubly Lee-Courant” (DLC) scheme, which enforces a local 𝜋 spin phase advance across every consecutive pair of snakes. Our analysis reveals a clear performance hierarchy, with the DLC configuration providing an exceptionally robust and energy-insensitive baseline for polarization preservation. We conclude that a hybrid strategy, using a DLC snake scheme as a symmetric foundation and betatron phase tuning for fine corrections, offers the most effective path forward for the EIC and future high-energy polarized-beam facilities.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗